Genetic Algorithms in the Framework of Dempster-Shafer Theory of Evidence for Maintenance Optimization Problems

Abstract

The aim of this paper is to address the maintenance optimization problem when the maintenance models encode stochastic processes, which rely on parameters that are imprecisely known, and when these parameters are only determined through information elicited from experts. A genetic algorithms (GA)-based technique is proposed to deal with such uncertainty setting; this approach requires addressing three main issues: i) the representation of the uncertainty in the parameters and its propagation onto the fitness values; ii) the development of a ranking method to sort the obtained uncertain fitness values, in case of single-objective optimization; and iii) the definition of Pareto dominance, for multi-objective optimization problems. A known hybrid Monte Carlo-Dempster-Shafer Theory of Evidence method is used to address the first issue, whereas two novel approaches are developed for the second and third issues. For verification, a practical case study is considered concerning the optimization of maintenance for the nozzle system of a turbine in the Oil & Gas industry.

Uncertainty treatment in expert information systems for maintenance policy assessment

“…In this respect, a novel method has been proposed by the authors to compare the couples of Belief and Plausibility measures corresponding to two different solutions [52]. On this basis, an advanced extension of the Genetic Algorithms technique has been concocted to optimize maintenance problems in the presence of imprecision [28].  Very large memory demand and computational times are required.…”

“…In practice, this multi-objective optimization problem has to be faced in a situation in which some constraints and/or the objective functions are affected by uncertainty. To effectively tackle this problem, a number of approaches have been already propounded in the literature considering different framework for uncertainty representation: probability distributions in [22]- [24], fuzzy sets in [25] and [26], and plausibility and belief functions in [27], [28].…”

Genetic algorithms for condition-based maintenance optimization under uncertainty

“…In fact, as pointed out in [17] and in [49], few approaches have been propounded in the literature to effectively tackle such multiobjective optimization problems in the presence of uncertain objective functions. These works consider different frameworks for uncertainty representation: probability distributions in [17], [23], [39], [49], [52], [57] fuzzy sets in [31] and [56], and plausibility and belief functions in [14], [33].…”

“…Now, the aim of the present work is to propose an extension of Multi-Objective Genetic Algorithms (MOGA [14], [27], [35], [38], [43]) to tackle the maintenance optimization issue when the epistemic uncertainty in the degradation model is represented in the probability theory framework. Namely, the parameters of the stochastic model of the degradation mechanisms are supposed to be Maximum Likelihood (ML)-estimated and the uncertainties in these estimations are represented by probability distributions [4], [25], [48].…”

“…In this work, we propose the pairwise ranking technique propounded in [10] and [14], and a Pareto dominance concept based on the ranks of the solutions. These concepts are combined with the NSGA-II elitist technique ( [16]), which relies on the Pareto dominance to effectively divide the evolving populations into non-dominated fronts of different ranks, thus allowing for a significant reduction in the computational times.…”